1. Introduction
Lithium-ion (Li-ion) batteries play a pivotal role in electric vehicles, consumer electronics, energy storage, and renewable energy systems. They offer higher energy density (23–70 Wh/kg), a lower self-discharge rate, relatively high cell voltage, and durability [
1]. However, their use and exposure to environmental conditions can degrade performance. This adversely affects their ability to store energy, meet power requirements, and eventually shorten their lifespans. Thus, the detection and characterisation of cell degradation are crucial for improving the battery performance, lifespan, and reliability of the systems that employ them. The characterisation of cell degradation is also vital in determining a cell’s suitability for second-life applications and can help shape the future of battery manufacturing.
Degradation of Li-ion cells is caused by the interaction between a myriad of physical and electrochemical processes. These processes are complex and occur across overlapping timescales, complicating their study. Capacity fade and an increase in internal impedance are known indicators of degradation [
1,
2,
3]. The ohmic resistance encompasses the internal resistance of components such as electrodes and electrolytes, while the capacitance is related to the dielectric properties of the electrolyte. Various techniques, including Electrochemical Impedance Spectroscopy (EIS), have been used to measure these parameters. EIS is a well-established impedance measurement method that has proven effective in studying degradation mechanisms and dynamic battery characteristics, such as mass transport processes [
4], internal impedance measurement [
1,
2,
5], and the formation of a Solid Electrolyte Interface (SEI) layer [
2].
Reflectometry is another well-established technique for detecting and characterising impedance discontinuities. It operates by sending high-frequency electromagnetic waves of various frequencies through a system or material. Depending on the impedance of the systems or materials under test, part of incident signal is reflected, and part is transmitted through it. System impedance characterisation is performed by analysing the reflected and transmitted signals. There are several forms of reflectometry, each of which is distinguished by the type of the incident signal used. In previous studies [
6,
7,
8], time-domain reflectometry (TDR), frequency-domain reflectometry (FDR), and spread-spectrum time-domain reflectometry (SSTDR) were effectively employed to detect and locate impedance irregularities in power lines (both overhead and subsea) and aircraft cables. FDR has also been used to measure the dielectric permittivity of soils and materials. In Masrakin et al. [
9] and Skierucha and Wilczek [
10], a resonator circuit based on FDR was designed such that its resonance frequency changed with the material being tested. By measuring the shift in the resonant frequency of the different dielectric materials, their respective capacitances and dielectric permittivity were determined.
Recent developments have extended reflectometry-based techniques to battery systems, notably in applications such as the assessment of batteries for power line communication (PLC) [
11,
12,
13] and the evaluation of battery electromagnetic interference and compatibility (EMI/C) [
14]. In such applications, the high-frequency characteristics of batteries in megahertz regions, which are typically outside the typical EIS range, are assessed. In Talie et al. [
12] and Bolsinger et al. [
13], while exploring the potential of using batteries as part of the communication channel in battery management systems (BMS), FDR was used to determine the high-frequency impedance of cells between 300 kHz and 30 MHz and 1–110 MHz, respectively. These studies characterised cells using equivalent models based (EEC) on high-frequency impedance measured using the reflection coefficient (S
11) method. However, the reflection method is less sensitive to impedance values of less than 1 Ω [
15]. Therefore, this configuration is not ideal for detecting aging-associated impedance changes in batteries that tend to be small in magnitude. The more sensitive shunt-through method, outlined in Keysight Technologies [
15] was used in Landinger et al. [
16] to measure the transmission parameters S
21 of Li-ion cells from 1 kHz to 300 MHz. Similarly, an EEC model that is based on the measured impedance was developed for cell characterisation. This was further used to compensate for the effects of mounts used in the setup. Based on the methods proposed in Landinger et al. [
16], the authors in Hackl et al. [
17] developed a generalised de-embedding method for use with a shunt-through setup when measuring the S
21 parameters of the batteries. This method addresses the inconsistencies that arise when cells are mounted on specialised PCB connectors for connection to Vector Network Analysers (VNA). The PCB connectors consist of a battery holder mounted on a PCB board with two subminiature version-A (SMA) connectors for connection to VNAs [
16]. In this method, the effects of the PCB connectors were removed by applying open, short, and load (OSL) impedance compensation to the measured data. The initial measured impedance obtained from the VNA that is calibrated using standard short, open, load, and through (SOLT) included influences from external mutual inductance between cells and the connectors, which was also compensated for by OSL compensation. In a study of the electrophysical processes of a cell at high frequency, Landinger et al. [
11,
18] employed this method to de-embed cell impedance from the measurement setup. An EEC model based on de-embedded impedance was developed, through which processes such as skin effects, ionic shunts, and resistive–inductive effects were identified. Furthermore, this study highlighted the dependency of high-frequency impedance on temperature, cell geometry, and design factors, such as winding and tab positions. The State-of-Charge (SoC) showed minimal influence on the measured impedance at frequencies up to 1 MHz.
These studies have applied high frequencies to measure battery impedance and have advanced knowledge by improving measurement setups, de-embedding protocols, modelling, and exploring impedance dependencies on temperature, SoC, and cell design. However, these tests have been carried out on either a single cell or a few cells, which raises the question of the universality of the method. Furthermore, these studies do not explicitly investigate the application of high-frequency impedance measurements for battery State-of-Health (SoH) estimation, nor do they evaluate the impact of SoH on the measured high-frequency impedance. It is noteworthy that the application of impedance measure to assess battery health has been studied in the literature, but these studies have been limited to lower frequency ranges and typically employed the EIS method [
5]. Battery aging can cause various physical changes in the battery, which can influence the measured impedance, particularly at high frequencies. In Roy and Khan [
19], the SSTDR method was applied to locate the degraded cells within a cell string. By establishing an initial reference when all cells in the string are healthy, aged cells are detected by the deviation of the subsequent measurement from the initial reference using sine-modulated pseudo-noise (SMPN) signals centered around 48 MHz. The effectiveness of this method in detecting the specific location of degraded cells in a series-connected lithium-ion battery pack shows deviations in measured high-frequency impedance from aging. However, the impact of battery strings on cells at various aging levels was not explored.
Therefore, this study investigates the use of FDR to monitor cell SoH by identifying the correlation between cell health indicators such as capacity and internal resistance and FDR impedance. This study differs in terms of the approach to utilising measured impedance. While previous studies solely focus the on measurement of impedance this study seeks to correlate the measured impedance with health indicators such as capacity and EIS-measured ESR to monitor battery SoH. This method has the potential to improve cell SoH characterisation by harnessing the ability of FDR to measure impedance and dielectric permittivity over a wide frequency range. The objective of this study is two-fold: First, to measure the high-frequency (HF) impedance of 19 cells exhibiting different levels of aging between 300 kHz and 1 GHz. This is accomplished using a setup based on both the S21 and ring resonator methods. Second, the aim was to apply the OSL compensation method proposed in the literature to de-embedding the cell impedance from the setup and perform a comparative analysis between results obtained before and after the de-embedding process was applied to the measured data. Additionally, a resonance-based method used in ring resonators was explored to investigate the relation between changes in cell resonance and cell dielectric permittivity. Cell capacity and internal resistance were obtained from cyclic aging and intermittent EIS testing.
The remainder of this paper is organised as follows.
Section 2 presents the research methodology, the cell aging processes, and test setups for the EIS and FDR tests. In addition, de-embedding and the definition of the region of confidence are described in this section.
Section 3 discusses the results and presents a comparative analysis of the resonance method with the responses obtained before and after the de-embedding process applied to the measured data. Finally,
Section 4 presents the conclusions.
2. Materials and Methods
The samples used are 19 commercial LIR2032 coin cells rated 4.2 V, 40 mAh. The cells were composed of a lithium cobalt oxide (LiCoO
2) cathode and a graphite (C) anode coated on aluminum and copper current collectors, respectively [
20]. The cell separator was made of polyethylene (PE), which was soaked in an electrolyte composed of a blend of ethylene carbonate (C
3H
4O
3) and lithium hexafluorophosphate (LiPF
6) [
20]. With the separator placed between the coated cathode and the anode current collector foils, all three were rolled into a flat jelly roll, as shown in
Figure 1. The anode and cathode tabs were placed at opposite ends of the jelly fold.
Figure 1a, adapted from Woehrle [
21], illustrates the flat jelly roll arrangement of the electrodes and separator in the cell, and
Figure 1b shows an image of the internal structure of the LIR2032 cell, highlighting the tap positions.
Figure 1b was obtained by opening the cell in a Braun UNILAB glovebox.
Three experiments were performed concurrently on these cells: cell cycling, EIS, and FDR tests. The cells were aged through cycling, and EIS tests were performed to monitor impedance changes in the cells during aging and to characterise the degradation of the cells. The responses from the cycling and EIS tests provided the health indicators used to evaluate the performance of the FDR method. EIS and FDR tests were conducted intermittently after every 20th cycle during the cyclic aging process.
2.1. Cell Cycling
The constant current–constant voltage (CC–CV) method was used in cycling. This was performed at 25 °C with an end charge voltage of 4.2 V and a discharge cut-off voltage of 2.75 V. Initially, all cells underwent two cycles at a rate of 0.05C. This slow cycling ensured the initial formation of an SEI layer [
22]. This also ensured that the aging effects observed during the subsequent cycling tests were not due to factors related to inconsistent electrode–electrolyte interfaces among the samples. After the initial slow cycles, the samples were divided into two batches. The first batch, herein referred to as Batch A, underwent the next 60 cycles at a rate of 1C, while the remaining cycles were performed at a 2C rate. Concurrently, cells within the alternate cohort, designated as Batch B, were cycled at a rate of 2C after the initial two slow cycles. This was performed to introduce variability into the samples under investigation.
Furthermore, cells 18 and 19 of Batch A were exposed to high discharge currents during cycles 14–22 and 270–300, respectively. Cycling was performed using a Maccor 4200 cycler, with the cells placed in a Binder FD 115 environment chamber for temperature control. Overall, 19 samples were aged for 102–442 cycles. The numbers of sample cycles and capacities are listed in
Table 1.
2.2. EIS Tests
EIS tests were performed on cells at 4.2 V, between 10 MHz and 100 kHz, with a test signal amplitude of 10 mV. An Autolab 302 N potentiostat was used for testing. All cells underwent a potentiostatic hold prior to testing. During the potentiostatic hold, the cells were held at 4.2 V until the current was below the rate of 0.01C (0.4 mA) to ensure that the cell voltage was stabilised before testing [
22]. To characterise cell aging, the impedance response from EIS tests was fitted to an equivalent circuit model (ECM) using the custom built EISyfit software, 2021 version used in Perry and Mamlouk [
4]. The parameters of the model were determined via local search and genetic algorithms. From the models, electrochemical processes such as charge transfer resistance, double layer capacitance, and resistance associated with SEI growth, which are known factors of aging, were identified and quantified. In addition, the equivalent series resistance (ESR), which represents the total internal resistance of the battery, was extracted from the impedance response.
2.3. FDR Measurement Setup
The VNA was employed in FDR impedance measurement [
11,
15,
16]. Specifically, the VNA two-port shunt-through method was used to measure the S-parameters of the cells, which were then converted into impedance. Although all four S-parameters were measured, only the transmission coefficient (S
21) was considered in this study. This offers more sensitivity in low ohmic measurements compared to other S-parameters [
13,
15]. The S
21 method is also equivalent to the four-terminal Kelvin-sensing method used in tests to eliminate the effects of test leads and unwanted resistance [
15]. Shown in
Figure 2a is the VNA measurement circuit for S
21 measurement. V
s is the VNA signal source whose current is limited by the series-connected 50 Ω resistor. Part of the source current is measured using the parallel-connected voltage sensor V
in and a 50 Ω resistor. This is compared with the transmitted signal for magnitude and phase calculations. As the current propagates through the circuit, a voltage drop occurs across the cell. This voltage drop is picked up by the port 2 voltage sensor V
T, which represents the measured S-parameters of both the cell and the connector PCB.
The connector PCB was used to connect the cells to the VNA, shown in
Figure 2b. The design uses two SMA connectors and a coin cell holder mounted on the PCB. These are connected such that the positive terminal of the cell holder connects to the inner pin of the SMA via the bottom plane of the PCB and the negative terminal connects the outer pins of the SMA through the top plane of the PCB. In addition to being suitable for S
21 measurements, this PCB design was also based on the resonator design used in Masrakin [
9]. The Pico106 VNA was used for FDR measurement. Prior to testing the cells, the VNA was calibrated using the short, open, load, and through (SOLT) calibration method. This was performed for a frequency range of 300 kHz to 1 GHz, with a source voltage of 0 dBm. The source voltage was chosen to attain a balance between measurement accuracy and cell linearity during the test. At 0 dBm, the dynamic range of the VNA was 90 dB, which ensured that the VNA could measure a wider range of signal levels. Thus, it can detect signals ranging from the VNA average noise floor level of −118 dB to signals of 90 dB or higher. As performed during the EIS test, the cells were placed in a prior potentiostatic hold before FDR tests.
The measured S
21 parameter is defined as the ratio between V
in and V
T, as expressed in Equation (1) [
23]. From this, the impedance was determined using Equation (2) [
24]. In Equation (1), V
transmitted refers to the transmitted voltage measured at port 2, and V
incident refers to the incident voltage coming from port 1. Both voltages are complex values whose amplitude and phase shifts (in degrees) are measured by the VNA. Z
L is the complex impedance calculated from the S-parameters which, in this study, is the total impedance of the cell and PCB. Z
o is the system characteristic impedance established by the VNA manufacturer. The typical value of Z
o is 50 Ω [
13,
18].
De-Embedding and Region of Confidence Definition
The SOLT calibration compensated for the effects of the VNA impedance and test leads during the measurement. This implies that the measurement reference point is at the end of the leads; therefore, the impedance calculated from Equation (2) is the impedance of the cell plus that of the connector PCB, herein referred to as Z
cell-in-pcb. To obtain the cell impedance only, Z
cell, the de-embedding method suggested in Hackl [
17] was adopted. In this method, a matched load of 50 Ω is connected in place of the cell, and its S-parameters (S
load) are measured using the SOLT-calibrated VNA. Similarly, the S-parameters of a copper coin (S
cu) were measured. The copper coin was fabricated to have the same dimensions as the LIR2032 cell such that it possessed a similar range of external inductance values. The PCB was then measured with the cell holder terminals open and short-circuited to obtain S
open and S
short, respectively. Equation (2) was applied to S
load, S
cu, S
open, and S
short to obtain Z
load, Z
cu, Z
open, and Z
short, respectively.
Equation (3) was applied to shift the measurement reference point to the positive terminal of the cell holder [
17]. This was performed for the cells and copper coin to obtain Z
cell-ext and Z
cu-ext, respectively. Z
sL is the ideal value of the match load, that is, 50 Ω. Z
inpcb is replaced by Z
cell-in-pcb to obtain Z
cell-ext, which includes the impedance of the cell and external inductive coupling effects between the cell and PCB planes. A similar procedure was performed using Z
cu to obtain Z
cu-ext. Using Equation (4), the effect of the external coupling between the cell and PCB planes is removed.
In Hackl et al. [
17], a region of confidence (RoC) was defined as the region within the spectrum where the open-circuit (Z
open) and short-circuit (Z
short) responses were the highest and lowest impedance values, respectively, and the load response (Z
load) was relatively closer to the open circuit than the short circuit. In this region, a cell with a relatively low impedance is expected to be closer to the short-circuit response. In this study, we added to this definition by identifying sections of the spectrum where changes in passive element responses were related to the changes in values of the respective element being measured. The RoC was defined for both the pre- and post-compensation stages using different values of resistors (R), inductors (L), and capacitors (C). Because this work involves the detection of changing values, this method of RoC definition helps to identify how the method detects changing values of resistive, inductive, and capacitive properties. This was performed for each analysis stage to identify the RoCs for each method and assess the overall setup sensitivity. For ease of reference, FDR impedance measured before the de-embedding process is herein referred to as pre-compensation, and impedance after the de-embedding is referred to as post-compensation.
First, the resonance-based method is used on the RLC responses obtained before de-embedding. Before de-embedding, resonance resulted from interactions between the PCB and inserted components, similar to those obtained in Masrakin et al. [
9]. The resonance frequency shifted with the changing values of the elements. Hence, the variations in the resonance frequency can be related to the type and value of the element under test, as illustrated in
Figure 3. The resonance frequencies of the inductors and capacitors decreased as their respective values increased. This was observed between 2 MHz and 130 MHz for inductors and between 4 MHz and 355 MHz for capacitors, as illustrated in green traces in
Figure 3b and
Figure 3c, respectively. This aligns with the inverse relationship between the resonance frequencies and the square root of the inductance and capacitance values. In contrast, the resonance frequency of the resistors, seen in
Figure 3a (green trace), remained relatively stable between 123 MHz and 130 MHz. The absence of resonance in the 100 Ω resistor within the test frequency region can be attributed to its high impedance, which makes it behave like an open or overdamped circuit at the frequencies of interest. The changes observed in the resonance frequency of capacitors are particularly promising because cells behave like capacitors in their basic form. However, the sensitivity decreases with increasing capacitance. In the nano-Farads range, a 25 nF change in capacitance between 22 nF and 47 nF produced a 2 MHz change in resonance frequency, which was further reduced to 1 a MHz change in resonance frequency from 57 nF to 100 nF. This suggests that, for coin cells with typical capacitance ranges between µF and mF, as seen in
Table 1, this method might not be sensitive enough to detect changes in such value ranges.
Outside the resonance region, changes in RLC responses that relate to variations in element values were observed between 300 kHz and 40 MHz. This behaviour was observed in both the pre-compensation and post-compensation responses. Within this region, the most accurate values are recorded at 300 kHz and are summarised in
Figure 3a–c. A comparison between values obtained from pre-compensation and post-compensation responses and the calculated values at 300 kHz for each element are presented in
Figure 3a–c. Overall, the recorded post-compensation impedances showed higher deviations than the recorded pre-compensation impedances for all RLC elements. This is because the de-embedding process compensates for PCB effects relative to cases of open, short, and load values, which can lead to deviations, especially when measuring very low impedances. Moreover, the measurements of low element values at both the pre- and post-compensation stages resulted in higher errors, indicating that achieving accuracy in the ranges of 5–10 mΩ, 0.1–1 nH, and 10–200 pF might be difficult for the setup. This limitation could hinder the accuracy of the method in measuring some health indicators, particularly when small changes in quantity are involved. The RoCs were therefore defined to be between 300 kHz and 40 MHz for both pre- and post-compensation responses and between 2 MHz and 355 MHz for resonance-based analysis. Within these regions, there was improved sensitivity to variations in resistive, inductive, and capacitive changes but with limited accuracy. It is also noteworthy that the observed reduction in accuracy with the lowest values of elements and limited sensitivity at higher capacitance values may limit FDR performance when applied to the cells’ more complex system, even within the RoC.
4. Conclusions
In conclusion, this study investigated the utilisation of FDR as a potential tool for monitoring the SoH of batteries. A measurement setup based on the ring resonator and the S21 method with a VNA was used to determine battery impedance. To ensure accuracy, system calibration and de-embedding procedures were employed to mitigate any interference from the test setup. Firstly, tests on different values of resistors, inductors, and capacitors revealed changes in these values, which were accurately detected between 300 kHz and 40 MHz with reduced accuracy within 5–10 mΩ, 0.1–1 nH, and 10–200 pF value ranges. Resistors, inductors, and capacitors resonated between 2 and 355 MHz. The resonance frequency of capacitors and inductors decreased with increasing values, while that of resistors remained relatively stable. However, both pre- and post-compensation responses exhibited limited sensitivity and accuracy, particularly with higher capacitance and inductance values. Nineteen LIR2032 commercial sample cells were used in the study. These were subjected to cyclic aging using the CC–CV cycling method. The results indicated a clear degradation in battery performance over cycles, evidenced by capacity loss and increased ESR. EIS analysis confirmed the effects of aging due to electrolyte decomposition and SEI layer growth. While the resonance method lacked sensitivity for cell capacitance, it effectively identified patterns of resistance change over the different sample cells. Despite promising correlations between FDR reactance and ESR trends, challenges remain in achieving consistent sensitivity and accuracy, particularly post-compensation. While FDR presents itself as a promising prospect for lithium-ion battery SoH monitoring, further research is imperative to enhance its sensitivity and address practical limitations to reduce its susceptibility to system noise. By advancing FDR-based methodologies and integrating complementary approaches, such as improved de-embedding protocols and noise mitigation strategies, the potential for accurate and reliable battery health monitoring that incorporates dielectric permittivity detection could be realised.